An alternative point of view on Lepski's method

By Lucien Birgé. 2001

172 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/f341262b39a6c387fb17bfc3bd3e5d76c09aac6a

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Environmental Engineering

Citations in the corpus

Locally stationary long memory estimation (2009, unknown): “bandwidth selection in non-parametric regression (see [4]).”
High-dimensional analysis of semidefinite relaxations for sparse principal components (2008, background): “Recall from equation (4) that for a matrix A ∈ Rm×n, the operator norm induced by the vector norms lp and lq (on R m and Rn respectively) is defined by |||A|||p,q = max ‖x‖q=1 ‖Ax‖p, (51)”
Minimal Penalties for Gaussian Model Selection (2007, unknown): “In this paper, we pursue our study of model selection for Gaussian frameworks, as described in Birgé and Massart [11].”
Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function (2005, unknown): “Using the inequality due to Birgé (2001) on the quantiles of non-central χ(2) we have that χ̄−1 n−dn,a2(β/2) ≤ n− dn + a 2 + 2 √ (n− dn + 2a2) log(2/β) + 2 log(2/β).”
Information-Theoretic Limits on Sparsity Recovery in the High-Dimensional and Noisy Setting (2007, methodology): “(34b) More generally, the analogous tail bounds for non-central χ2, taken from Birgé [1], can be established via the Chernoff bound.”
Theory of classification : a survey of some recent advances (2005, unknown): “They are also discussed by Birgé [35].”
Oracle inequalities for inverse problems (2002, methodology): “For the direct case (where σk ≡ 1) such an inequality is obtained by Birgé (2001), who uses the Lepski adaptation method rather than the Mallows Cp.”
Anti-concentration and honest, adaptive confidence bands (2013, methodology): “We use Lepski’s method [26, 2] to find an adaptive value of the smoothing parameter.”
Minimax risks for sparse regressions: Ultra-high-dimensional phenomenons (2010, unknown): “(5.6) is a special case of Theorem 1 in Birgé and Massart [12].”
Confidence balls in Gaussian regression (2004, unknown): “These inequalities are due to Birgé (2001).”